There are two things I would like to cover here: breaking axis and starting axis at zero to show small/high differences between samples.
I am pretty sure there are various opinions on both of those issues and you might find one of them acceptable while not the other. My personal take is to avoid both.
Let's start with breaking the axis.
The idea behind using this trick is to be able to show low and high values on the same graph, like here from Leal et al. 2016:
But was it really necessary? If you don't pay close attention to the axis you may underestimate the difference between extracellular and intracellular measurements.
Here is how the graph would look like if the axis was not broken:
Not too bad, right? And you can still see differences, so it was completely unnecessary to break the axis. Of course not all data is like this, sometimes the differences will make one of the values unreadable. In that case you may want to present it as normalized to control or a fold change.
The second issue is to start your axis at zero.
Commonly starting an axis not at zero is used to emphasize the differences between the two sample which do not differ much. I do hope I don't really have to discuss it and you know it's unacceptable to do it.
Instead I will give an example from Frahm et al. 2017:
First of all, putting a table and a graph together is redundant. The idea behind using a graph is that you don't need a table anymore.
Second is the axis - I am sure you remember from your math class to draw the axis crossing at zero, not 1... I understand that the authors want to emphasize what is a decrease (below the axis) and what is an increase (above the axis), ergo the different crossing. It can be done even keeping the standard 0/0 cross.
Maybe you can see the similarity to gating from the flow cytometry graphs.
Alternatively you can use a very different design:
This however means you compromise the ability to show the correlation/regression curve.
What become obvious to me while redesigning this graph is that maybe there is something wrong with the data itself... I asked myself what is a fold change? Does fold change of 1 means there is no change (as shows graph from Frahm et al.) or a 100% increase?
Honestly, this is the main lesson I ended up taking from writing this post about the axis tricks - if you have to manipulate the axis, maybe you have to think about your data differently?